Wonders in flat bands: from quantum liquid crystals to self-correcting quantum memory
In this talk, I will discuss two cases where flat bands in frustrated lattice models lead to emergence of interesting physics.
In the first part, I talk about a family of interacting boson models based on a kagome lattice with local synthetic gauge flux, which can be realized in optical lattices with ultra-cold atoms or circuit-QED lattices with interacting photons. Such models have a lowest flat band in the single-particle spectrum. The flat band is spanned by eigenstates forming localized loops on the lattice, with the maximally compact loop states typically breaking the discrete rotational symmetry of the lattice. When populated by locally-interacting particles, the close packing of such maximally compact loop states leads to a nematic loop crystal ground state. We predict that increasing the filling beyond the close packing fraction leads to the formation of quantum liquid crystals including a nematic supersolid and a nematic superfluid phase. We also show how the nematicity can be probed by time-of-flight experiments or phase imprinting techniques .
In the second part, I discuss how 4-body spin interactions can emerge in a 2D flat-band lattice with “Aharonov-Bohm cages”, and in the presence of light-matter interactions. Based on such an idea, one can realize the surface-code Hamiltonian in the ultra-strong coupling regime of a circuit-QED lattice, when the interaction strength is comparable to the microwave photon frequency. Two types of 4-body stabilizer interactions are realized by utilizing the electro-magnetic duality in circuit-QED. In such case, the circuit-QED vacuum has topological degeneracies and can be used as a self-correcting quantum memory. An alternative approach without ultra-strong coupling is to simulate the surface-code Hamiltonian in the rotating frame, with side-band driving through modulating the flux penetrating SQUID couplers.
 Guanyu Zhu, Jens Koch and Ivar Martin, arXiv:1411.0043